Problem 1: A manufacturer of lawn care equipment has introduced a new product. The anticipated demand is normally distributed with a mean of µ= 100 and a standard deviation of s = 50. Each unit costs $75 to manufacture and the introductory price is to be $125 to achieve this level of sales. Any unsold units at the end of the season are unlikely to be very valuable and will be disposed of in a fire sale for $25 each. It costs $10 to hold a unit in inventory for the entire season. What is the optimal cycle service level? How many units should be manufactured for sale?
Problem 2: In the previous problem, the manufacturer performs additional market research. Based on this research, they determine that they can increase the price to $150 and are able to reduce the standard deviation of the forecast to s = 30. At the same time, they have made an arrangement with an outlet store that will purchase unsold equipment for $60 each. What are the optimal cycle service level and optimal order size, respectively?